We study a popular pencil-and-paper game called morpion solitaire.
We present upper and lower bounds for the maximum score attainable for many
versions of the game. We also show that, in its most general form, the game
is NP-hard and the high score is inapproximable within
n1 − ε
for any ε > 0
unless P = NP.

Christian Boyer maintains the latest Morpion results on morpionsolitaire.com. In particular, it is now known that G3(A3) = 35 and that G′3(A3) = 62 (lower bounds in "New Heuristics for Morpion Solitaire" by Heikki Hyyrö and Timo Poranen, and upper bounds by enumeration by Michael Quist). There is also a new lower bound of G4(A4) ≥ 82 (by Tristan Cazenave), proposed upper bound of G4(A4) ≤ 138, and a new lower bound of G′4(A4) ≥ 172 (by Christopher Rosin, beating the previous 34-year-old record by Charles-Henri Bruneau)